5 ideas
| 9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
| Full Idea: The terms 'set' and 'is a member of' are primitives of Zermelo's 1908 axiomatization of set theory. They are not given model-theoretic analyses or definitions. | |
| From: report of Ernst Zermelo (works [1920]) by Charles Chihara - A Structural Account of Mathematics 7.5 | |
| A reaction: This looks like good practice if you want to work with sets, but not so hot if you are interested in metaphysics. |
| 3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
| Full Idea: For Zermelo's set theory the empty set is zero and the successor of each number is its unit set. | |
| From: report of Ernst Zermelo (works [1920]) by Simon Blackburn - Oxford Dictionary of Philosophy p.280 |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| Full Idea: If, for the sake of argument, someone were to mould a horse, squash it, then make a dog, it would be reasonable for us on seeing this to say that this previously did not exist but now does exist. | |
| From: Mnesarchus (fragments/reports [c.120 BCE]), quoted by John Stobaeus - Anthology 179.11 | |
| A reaction: Locke would say it is new, because the substance is the same, but a new life now exists. A sword could cease to exist and become a new ploughshare, I would think. Apply this to the Ship of Theseus. Is form more important than substance? |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |